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Similarity of figures is a property that is used to compare figures. Two triangles are said to be similar if their corresponding sides are in equal ratio and if their corresponding angles are equal. If the corresponding sides of two triangles are equal, then these triangles are called equiangular triangles. In an equiangular triangle, the ratio of the corresponding sides of the two sides is always the same. This property of triangles follows from the basic proportionality theorem.
The CBSE is yet to announce the date for the supplementary exams. However, according to official reports, the supplementary exam date sheet is expected to be released in mid-July.
These NCERT solutions of Class 10 maths ex 6.2 contain two theorems: (Theorem 1) When a parallel line is drawn along one of the triangle's sides and intersects the other two sides at certain points, the two sides are divided in the same proportion. (Theorem 2) Any line that divides the two sides of a triangle in the same ratio is parallel to the third side. NCERT solutions for exercise 6.2 Class 10 Maths chapter 6 Triangles discuss the concept as per the NCERT Book, like a triangle as a polygon, the interior angles of a triangle, the exterior angles of a triangle, Pythagoras' theorem, and conditions of similarity in triangles.
Triangles Class 10 Chapter 6 Exercise: 6.2
Q1 In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).
Answer:
(i)
Let EC be x
Given: DE || BC
By using the proportionality theorem, we get
(ii)
Let AD be x
Given: DE || BC
By using the proportionality theorem, we get
Answer:
(i)
Given :
PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
We have
Hence, EF is not parallel to QR.
Answer:
(ii)
Given :
PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
We have
Hence, EF is parallel to QR.
Q2 (3) E and F are points on the sides PQ and PR respectively of a triangle PQR. For each of the following cases, state whether EF || QR : PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
Answer:
(iii)
Given:
PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
We have
Hence, EF is parallel to QR.
Q3 In Fig. 6.18, if LM || CB and LN || CD, prove that
Answer:
Given : LM || CB and LN || CD
To prove :
Since , LM || CB so we have
Also, LN || CD
From equations 1 and 2, we have
Hence proved.
Q4 In Fig. 6.19, DE || AC and DF || AE. Prove that BF / FE = BE / EC
Answer:
Given: DE || AC and DF || AE.
To prove:
Since , DE || AC so we have
Also, DF || AE
From equations (1) and (2), we have
Hence proved.
Q5 In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.
Answer:
Given: DE || OQ and DF || OR.
To prove EF || QR.
Since DE || OQ, we have
Also, DF || OR
From equations (1) and (2), we have
Thus, EF || QR. (Converse of the basic proportionality theorem)
Hence proved.
Answer:
Given: AB || PQ and AC || PR
To prove: BC || QR
Since, AB || PQ so we have
Also, AC || PR
From equations (1) and (2), we have
Therefore, BC || QR. (converse basic proportionality theorem)
Hence proved.
Answer:
Let PQ be a line passing through the midpoint of line AB and parallel to line BC, intersecting line AC at point Q.
i.e.
Using the basic proportionality theorem, we have
Since
Answer:
Let P is the midpoint of line AB, and Q is the midpoint of line AC.
PQ is the line joining midpoints P and Q of lines AB and AC, respectively.
i.e.
We have,
From equations (1) and (2), we get
Therefore, by the basic proportionality theorem, we have
Answer:
Draw a line EF passing through point O such that
To prove:
In
So, by using the basic proportionality theorem,
In
So, by using the basic proportionality theorem,
Using equations (1) and (2), we get
Hence proved.
Answer:
Draw a line EF passing through point O such that
Given :
In
So, by using the basic proportionality theorem,
However, it is given that
Using equations (1) and (2), we get
Therefore, ABCD is a trapezium.
Also Read-
1. Similar Figures: Two figures are said to be similar if their corresponding sides are in the same proportion and corresponding angles are equal.
2. Conditions for Similar Triangles: The criteria for similarity of the triangle are AA (Angle-Angle), in which two angles of one triangle are equal to the corresponding two angles of another triangle.
3. Midpoint Theorem: In this theorem, the line segment that joins the midpoint of the two sides of the triangle is parallel to the third side of the triangle, and the length of this line segment is half of the third side of the triangle.
4. Parallel Lines and Transversals: A transversal divides the sides of the triangle into proportional segments when it intersects the two parallel lines.
Also see-
Students must check the NCERT solutions for Class 10 Maths and Science given below:
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:
The term "similar" refers to two figures that have the same shape but differ in size.
The congruent figures are all similar, but the opposite is not true.
If we know the side ratio and the length of any side, we can find the length of the corresponding side of the other triangle by using the ratio.
The ratio of the areas of the triangles is equal to the square of the ratio of the sides.
The ratio of the areas of the triangles is equal to the square of the ratio of the sides.
Ratio of area = 1:4
4/x=1/3
x=12cm
The length of the longer side is 12cm.
It will always be parallel to the third side of the triangle.
No, resemblance only relates to the shape of the figures and does not imply equality.
Admit Card Date:17 April,2025 - 17 May,2025
Admit Card Date:06 May,2025 - 20 May,2025
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters